> The intuitive meaning is that a day is 24 hours
Ok so far.
> and you can divide that by 60 twice
I'm not so sure. The concept of 24 hours in a day originates in civil timekeeping, yes, but not minutes and seconds. Those originally came from astronomy, and corresponded to angles, not times, and those angles are constants; they don't change as the Earth's rotation slows down or as its speed in orbit around the Sun changes over the course of a year. I don't think people's intuitive concept of minutes and seconds is that they vary according to the time of year or the tidal effects on the Earth.
Ok so far.
> and you can divide that by 60 twice
I'm not so sure. The concept of 24 hours in a day originates in civil timekeeping, yes, but not minutes and seconds. Those originally came from astronomy, and corresponded to angles, not times, and those angles are constants; they don't change as the Earth's rotation slows down or as its speed in orbit around the Sun changes over the course of a year. I don't think people's intuitive concept of minutes and seconds is that they vary according to the time of year or the tidal effects on the Earth.